Chemical–Gravity–Thermal Diffusion Equilibrium in Two-Phase Non-isothermal Petroleum Reservoirs

Abstract

The initial state of hydrocarbon mixtures in petroleum reservoirs is the result of equilibrium among several forces, the most important of which are the chemical forces arising from chemical potential gradients of the molecular species in the petroleum accumulation, the gravitational force arising from the gravitational acceleration, and the thermal diffusion forces arising from temperature gradients. The equilibrium among these forces determines the state of pressure and a compositional gradient and the creation of a gas–oil contact (GOC) in a stationary reservoir along with the changes in other physical properties. Accurate modeling of these changes in the development of a proper stationary model for the reservoir simulation initialization leads to more realistic predictions of the future behavior of petroleum reservoirs. This is important especially when phase behavior is important in designing, modeling, and predicting the performance of the processes used to maximize the oil recovery, such as in dealing with a gas condensate reservoir or when miscible displacement is to be done in the enhanced oil recovery (EOR) stage of the reservoir life. In this study, we consider the equilibrium among chemical, gravitational and thermal diffusion forces to predict the changes in reservoir fluid composition and pressure and also to predict the location of a possible GOC in a reservoir. Additionally, we develop a simple model to predict the change of the plus-fraction molecular weight (MW) in a non-isothermal reservoir using continuous thermodynamics and the theory of irreversible processes. We propose a method not only to tune the equation of state (EOS) versus the measured PVT lab data for one fluid sample but also to accurately model the depths of the GOC and other fluid samples and their PVT lab data in order to determine which sample is representative of the reservoir fluid and also to develop an EOS model that can work for every fluid in the reservoir, not just a single point. In two case studies, we validate our calculation procedure for the general compositional gradient, GOC detection, and the plus-fraction MW change in the reservoir against two data sets from the literature. The computational results show that the model developed works satisfactorily to predict the fluid changes in these two reservoirs. Subsequently, we also report the results of a series of sensitivity analysis tests to show the factors affecting the compositional gradient calculations and present examples of abnormal fluid distributions in a hydrocarbon fluid column where the fluid becomes denser toward the top of the column or the changes in fluid properties are highly nonlinear with respect to depth in the reservoir.

An Efficient Method to Predict Compressibility Factor of Natural Gas Streams

“…Fluid properties are directly involved in all flow and volumetric calculations in the upstream and downstream zones of the petroleum industry. Density and its change over pressure, vaporization, or condensation ratios, as well as kinetic properties such as viscosity all affect the obtained results [1][2][3][4].…”

Analytical solution for compositional profile driven by gravitational segregation and diffusion

“…As the injected fluid changes the pressure distribution in the reservoir a careful consideration of the vertical compositional gradient has to be carried out [14,16] to ensure that the requirement for miscibility is achieved at all depths. Temperature, which also increases with depth in most reservoirs, can also drive segregation of components through temperature diffusion (the Soret effect), [17][18][19][20] sometimes counteracting the gravity driven segregation. Typically, temperature has the greatest effect when there is also a horizontal temperature gradient which may alter the compositional distribution via natural convection or when the system is near its critical point [5,17,[20][21].…”

“…Over the years a number of models [5,16,[19][20][21][22][23][24][25][26][27] and references therein] have been developed to predict the distribution of components within the oil reservoirs. Most models have focussed on predicting the vertical distribution of components, although some have also examined the 3D distribution [17,18,27].…”

“…Most models have focussed on predicting the vertical distribution of components, although some have also examined the 3D distribution [17,18,27]. The level of sophistication varies from models assuming an isothermal reservoir to those considering thermal diffusion, convection, external fluxes and biochemical degradation [5,16,[19][20][21][22][23][24][25][26][27]. The general aim is to predict how compositional profiles change over geological time--2 -scales, the steady-state profile and to estimate time scales to reach steady-state.…”

“…The general aim is to predict how compositional profiles change over geological time--2 -scales, the steady-state profile and to estimate time scales to reach steady-state. Although large advances have been made [17][18][19][20][21][22][23][24][25][26][27][28][29][30], the lack of experimental thermophysical data, the incomplete characterization of geological heterogeneities, unknown boundary and initial conditions and incomplete understanding of some of the processes have led to only moderate success in predicting the observed distributions in composition, even when fully general numerical simulators are used. It is therefore useful to have range of simple analytical solutions that can be used to predict end member cases and thus bound the compositional profiles that may be expected in different circumstances, as well as to validate numerical simulations.…”